International Journal of Wireless Communications and Mobile Computing 2016; 4(1): 7-11

Published online March 9, 2016 (http://www.sciencepublishinggroup.com/j/wcmc)

doi: 10.11648/j.wcmc.20160401.12

ISSN: 2330-1007 (Print); ISSN: 2330-1015 (Online)

Performance Evaluation of Variant Error Correction Schemes in Terms of Extended Coding Rates & BER for OFDM Based Wireless Systems

Md. Nurul Mustafa, Mohammad Jahangir Alam, Nur Sakibul Huda

Department of Computer Science and Engineering (CSE), Southern University Bangladesh, Chittagong, Bangladesh

Email address: nurul.mustafa@southern.edu.bd (Md. N. Mustafa), jahangir@southern.edu.bd (M. J. Alam), jetsakib@yahoo.com (N. S. Huda)

To cite this article: Md. Nurul Mustafa, Mohammad Jahangir Alam, Nur Sakibul Huda. Performance Evaluation of Variant Error Correction Schemes in Terms

of Extended Coding Rates & BER for OFDM Based Wireless Systems. International Journal of Wireless Communications and Mobile

Computing. Vol. 4, No. 1, 2016, pp. 7-11. doi: 10.11648/j.wcmc.20160401.12

Abstract: Modern OFDM systems provide effective spectral usage by allowing overlapping in the frequency domain.

Moreover, it is highly resistant to multipath delay spread. The suppression of inter-symbol interference (ISI) is one of the top

features of OFDM. It also facilitates mobile bandwidth allocation and may increase the capacity in terms of number of users.

Even though the presence of OFDM’s built in error preventing mechanism; error tends to occur that averts delivery of proper

signal. In this work we evaluated and adapted ways of fine-tuning for different error correction methods so that they may bring

positive impact on communication systems who are developing and using OFDM. Here the performance of different known

error correcting techniques for OFDM systems have been analyzed after extending and puncturing feature is applied on them.

Simulations are performed in well-known simulator MATLAB to evaluate the modified techniques for different channel

conditions. As the advantage of OFDM based systems are mainly the robustness to channel impairments and narrow-band

interference; thus added error reduction models will improve significant efficiency of systems based on OFDM.

Keywords: Extended RS Code, AWGN, ISI, BER, Extended Convolution Code, Extended LB Code, FFT, IFFT

1. Introduction

Wireless communication, as the name suggests [1], is

wireless way of transmitting information from one place to

another, is replacing most of the wired transmission of

today’s world. Research in the field of wireless

communication is still a hot topic to discover new

possibilities. The goal of every research in this topic is to find

more effective communication methods. Wireless

communication helped the user to move freely without

worrying about transfer of data. It dramatically changed the

concept of information transfer in homes and in offices.

The basic building blocks of a typical wireless

communication system [2], are encoder, channel coder,

modulator, demodulator, and channel decoder. The signal is

first converted to digital data and then source encoded.

Source encoding reduces the amount of the data present in

the signal to reduce the bandwidth required to transmit the

associated data. Then the data proceeds to channel encoder

block, which is responsible for adding extra bits in the data to

help correcting errors inflicted to the data due to fading and

noise. Our work in this paper contains three techniques for

channel encoding that will be explained in later chapters. The

modulator modulates the message signal on the transmission

frequency so that the signal is ready for transmission.

Signal when transmitted, through wireless channel, faces

multiple problems [3]. One major problem faced by the

signal is fading. Fading can be caused by natural weather

disturbances, such as rainfall, snow, fog, hail and extremely

cold air over a warm earth. Fading can also be created by

manmade disturbances, such as irrigation, or from multiple

paths. All these factors introduce errors into the transmitted

data.

When received at the receiver the signal is added with

noise, since receiver antenna is designed to receive any signal

present within a certain frequency range and noise is also

present in that range. Now that data is passed to the

demodulator whose job is convert the signal back from the

carrier frequency to its normal form. After that the channel

decoder helps to recover original signal from the degraded

signal due to channel fading and noise. This is done by using

the redundant bits that were added by the channel encoder.

8 Md. Nurul Mustafa et al.: Performance Evaluation of Variant Error Correction Schemes in Terms of

Extended Coding Rates & BER for OFDM Based Wireless Systems

This signal after recovery is passed to the source decoder,

which converts the signal back to its original form.

2. The Problem in Details

OFDMis a technique, for transmission of data stream over

a number of sub-carriers. In OFDM, a high rate bit stream is

divided into bit streams of lower rate and each of them are

modulated over one of the orthogonal subcarriers [1]. In a

single carrier system a single fade can cause the entire link to

fail while in a multi carrier system only a few bits will be

disturbed and they can be corrected by applying error

correction codes.

OFDM overcomes the problem of inter-symbol

interferenceby transmitting a number of narrowband

subcarriers together with a guard interval [4]. But this gives

rise to another problem that all subcarriers will arrive at the

receiver with different amplitudes. Some carriers may be

detected without error but the errors will be distributed

among the few subcarriers with small amplitude.

Channel coding can be used across the subcarriers to

correct the errors of weak subcarriers. In OFDM systems

error correction has a significant role since OFDM along

with error correcting techniques help to deal with fading

channels. Error correction helps in recovery of faded

information by providing a relation between information and

transmitted code such that errors occurring within the

channel can be removed at the receiver. A lot of such

techniques for error correction are given till date. In this

work some of these techniques are considered, modified to an

extent & implemented for OFDM system and then a

comparison between them are made for best outcome.

3. Channel Coding

Channel codingis basically from the class of signal

transformations designed to improve the communication

performance by enabling the transmitted signal to better

resist the effects of various channel impairments such as

noise fading and jamming [5]. The goal of channel coding is

to improve the bit error rate (BER) performance of power

limited and/or band limited channels by adding redundancy

to the transmitted data. The three channel coding schemes

[13], that are modified to achieve objective of this work are

described in the following section:

3.1. Linear Block Coding

A block code is defined as a code in which k symbols are

input and n symbols are output and is denoted as a (n, k)

code[5]. If the input is k symbols, then there are 2k distinct

messages. For each k input symbols output is n symbols

known as a codeword where n is greater than k. Figure 1

shows input and output of a block code and the size of

codeword formed.

A block code of length n with 2 kcodewords is called a

linear (n, k) code if and only if its 2 kcodewords form a k-

dimensional subspace of the vector space of all n-tuples over

the Galois field GF. Since there are n output bits so there are

2n combinations possible for codewords but all of them are

not codewords rather 2k are codewords. Rest of the

combinations usually comes forward when there is an

erroneous transmission and codewords are corrupted by

change in bits. There are some rules which codewords have

to fulfil. One of them is that the sum of any two codewords is

also a codeword and being a linear vector space, there is

some basis, and all codewords can be obtained as linear

combinations of the basis [6]. Anexample of [5] code is

generated by generator matrix given below:

G =�1 0 0 0 0 1 10 1 0 0 1 0 100 00 1 0 1 1 00 1 1 1 1�

Figure 1. A block encoder and a LB coding codeword.

3.2. Convolution Code

Convolutional codes are different from the block codes

[7], since in convolutional coding the information sequences

are not grouped into distinct blocks and encoded so a

continuous sequence of information bits is mapped into a

continuous sequence of encoder output bits. Convolutional

coding can achieve a larger coding gain than can be achieved

using a block coding with the same code rate [8].

Convolutional codes have their popularity due to good

performance and flexibility to achieve different coding rates.

An important characteristic of convolutional codes [9] is

that the encoder has memory. That is the n-tuple output

generated by the encoder is a function of not only the input

k-tuple but also the previous N-1 input k-tuples. The integer

N is called the constraint length [7]. The convolutional

code is generated by passing the information sequence

through a finite state shift register. In general, the shift

register contains N stages and m linear algebraic function

generators based on the generator polynomials [9]. The

input data k bits is shifted into and along the shift register.

The number of output bits for each k input bits is n bits. The

code rate is given as R= k / n.

3.3. RS Coding

The mechanism by which Reed-Solomon codes [10]

International Journal of Wireless Communications and Mobile Computing 2016; 4(1): 7-11 9

correct errors is that the encoder adds redundant bits to the

digital input data block. The decoder attempts to correct

and restore the original data by removing the errors that

are introduced in transmission, due to many reasons that

might be the noise in the channel or the scratches on a CD.

There are different families of Reed-Solomon codes and

each has its own abilities to correct the number and type

of errors.

These codes are linear and a subsection of BCH codes [11]

and can be denoted as RS(n, k) with s-bit (Where s are

symbols represented as a bit) symbols.

An n-symbol codeword is made by the k data symbols of s

bits each and the encoder adds parity bits. Errors in a

codeword can be corrected by the decoder up to t symbols

where, 2t=n-k.

4. Research Methodology

Quantitative research methodology (AI-Mahmoud &

Zoltowski, 2009) is adopted in this work. MATLAB is used

as a tool to implement the OFDM system, error correcting

techniques for the OFDM system and after that a

performance comparison is made between these techniques.

The outcomes of this work will be a BER (Bit Error Rate) vs.

SNR (Signal to Noise Ratio) comparison, which will tell the

behavior of all these three codes (Linear block codes,

Convolutional codes and Reed-Solomon codes) under

different SNR. The assessment will help us to analyze the

performance of the three coding techniques in combination

with OFDM. The finding of this work may help the OFDM

system designers to choose the error correcting codes that

match their requirements.

4.1. Code Modification

A code C has three fundamental parameters. Its length n,

its dimension k, and its redundancy r = n-k. Each of these

parameters has a natural interpretation for linear codes, and

although the six basic modification techniques [3], are not

restricted to linear codes it will be easy initially to describe

them in these terms. Each of these one parameter and

increases or decreases the other two parameters accordingly.

We have:

1. Augmenting. Fix n; increase k; decrease r

2. Expurgating. Fix n; decrease k; increase r

3. Extending. Fix k; increase n; increase r

4. Puncturing. Fix k; decrease n; decrease r

5. Lengthening. Fix r; increase n; increase k

6. Shortening. Fix r; decrease n; decrease k

The six techniques fall naturally into three pairs, each

member of a pair the inverse process to the other. Since the

redundancy of a code is its “dual dimension” each technique

also has a natural dual technique. In this workwe used the

extending feature of code modification. We have modified

our OFDM input & output code correction techniques

according to the extended features and performed the

simulation accordingly.

4.2. Extending & Puncturing

In extending or puncturing [5] a code we keep its

dimension fixed but vary its length and redundancy. These

techniques are exceptional in that they are one-to-one. Issues

related to the extending and puncturing of GRS codes will be

discussed in the next two sections.

When extending a code we add extra redundancy

symbols to it. The inverse is puncturing, in which we

delete redundancy symbols. Puncturing may cause the

minimum distance to decrease, but extending will not

decrease the minimum distance and may, in fact, increase

it. To extend a linear code we add columns to its generator

matrix, and to puncture the code we delete columns from

its generator.

Let us call the [n + 1, k] linear code C+ a coordinate

extension of C if it results from the addition of a single new

redundancy symbol to the [n, k] linear code C over the field

F. Each codeword c+ = (c1,….., cn, cn+1) of the extended code

C+ is constructed by adding to the codeword c = (c1,……,cn)

of C a new coordinate ���� = ∑ �� � = �. ���� , for some

fixed a = (a1,……,an) ϵ Fn. Here I imply that the new

coordinate is the last one, but this is not necessary. A

coordinate extension can add a new position at any place

within the original code.

The most typical method of extending a code is the

appending of an overall parity check symbol, a null symbol

chosen so that the entries of each new codeword sum to zero.

This corresponds to a coordinate extension in which ‘a’ has

all of its entries equal to -1.

5. Simulation & Results

To keep the conditions same for all the simulations the

input data, the fading channel and the noise is once generated

and saved. The input data is kept same for testing of all

coding schemes. The total number of carriers [12] chosen in

the OFDM system is 128 and used is 104. Eb/No (Energy per

bit to noise power ratio) is used in testing. Eb/No is useful

when comparing BER in digital modulation schemes without

taking the bandwidth into account.

Rayleigh fading channel is once generated and saved. The

same fading is used for all the simulations. The fading is

defined by the following MATLAB equation: rayleigh = sqrt(0.5 ∗ (randn(N, 1" + i ∗ randn(N, 1""" Where ‘randn()’ generates values from the standard normal

distribution function and ‘N’ defines the length of fading

signal.

The results of simulation for code rate of 1/3 as per

MATLAB simulation are shown in Figure 2. It is found

that convolution code after the extending & puncturing

features applied gives 2 dB improvement than Reed

Solomon Code and 4 dB improvement than flat Block

Codes at BER of 10-3

.

10 Md. Nurul Mustafa et al.: Performance Evaluation of Variant Error Correction Schemes in Terms of

Extended Coding Rates & BER for OFDM Based Wireless Systems

Figure 2. Convolutional encoder with length 7 & rate ½.

Figure 3. Comparison of Three Extended & Punctured Coding Schemes for

1/3 Code Rate.

Figure 4. Comparison of Three Extended & Punctured Coding Schemes for

1/2 Code Rate.

The results of simulation for code rate of 1/2 are shown in

Figure 3. It is found that RS code after the extending &

puncturing features applied gives 1 dB improvement than

Convolution Code and 2 dB improvement than Block Codes

at BER of 10-3

.

The final results of simulation for code rate of 2/3 are

shown in Figure 4. It is found that Convolution code after the

extending & puncturing features applied gives.5 dB

improvement than RS Code and 1.5 dB improvement than

Block Codes at BER of 10-3

.

Figure 5. Comparison of Three Extended & Punctured Coding Schemes for

2/3 Code Rate.

Hence from all the performance analysis made above for

different scenarios are shown in the following graphs:

International Journal of Wireless Communications and Mobile Computing 2016; 4(1): 7-11 11

Figure 6. Comparison of all three error rectification techniques in terms of

extended & punctured coding scheme for OFDM systems.

6. Conclusion

In this work it is found that Convolutional codes are very

good in performance at lower code rates but due to complex

decoding structure they are difficult to implement. Another

problem that may arise in them is error propagation while

decoding. Convolutional codes have problem of very

complex decoding so if the length of input data is increased,

the trellis used will be complex and the decoding will

become even more complicated.

Linear block codes are very simple to implement. They

also show good performance and are also good for lower

code rates and highly suitable for application with less

complexity requirement and not so high performance

requirement.

Reed-Solomon codes in comparison to linear block codes

are difficult to implement but their performance is much

better and consistent than linear block codes since they can

handle long bursts of errors. These codes showed good

performance on all three tested code rates.

Hence with the system that requires good performance and

along with that can also handle complexity, there is no better

than convolution code. But if the system can’t handle

complex architecture then RS codes might be more suitable

for the purpose.

7. Limitations

Limitation of this work certainly includes the use of a

model noise channel as this result is yet to be tested in

physical condition. If someone changes the generator matrix

then it will also change the results. Thus it is not possible to

generalize these results by having different environment

other than described in Section V in simulation environment.

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[6] Agarwal, Arun, & Patra, S. K. (2011). Performance Prediction of OFDM based DAB System using Block coding technique”, Proceedings of ICETECT, India.

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